Excessive oil consumption

2000 honda accord ex 4 cyl, 91000 miles. I am having a most disturbing time with my honda in that it seems to be burning about 4 quarts of oil every 3-4 weeks. Experiencing loss of power as well. Took it in to dealer and came up with code P1259 which they tell me is a vtec system fail at which time they changed oil and all was good for a little while. Took it to a different shop about a month later. Same code said car was low on oil again, good. Well about 3 weeks later same deal. This time mechanic did look for leaks, only a small one at the timing housing, checked for coolant condition, all good, did compression test all cyl wet + dry 3cyl fail more than 20% variance. 15% 20% 25% 36%. Told me most likely cause was piston rings but possibly valve seats or seals. Said I would be better off just dropping in new engine. Car is still under powertrain warranty up to 100,000 miles so took it back to dealer. They mentioned small leak at timing housing but after explaing to them that its burning that amount of oil they asked me to pick up car and drive it for 500-1000 miles to see for themselves how much oil it has burned. I asked them repeatedly about the results of compression test but they don't seem to believe me. Have noticed a lot of oil around tail pipe of exhaust. Are there any other things that could be causing car to burn this much oil? Or is the dealer just trying to avoid covering this under warranty.